w . m . w h i t e g e o c h e m i s t r y chapter 1:...

W . M . W h i t e G e o c h e m i s t r y

Chapter 1: Introduction

1 August 31, 1997


Geochemistryhe term ÒgeochemistryÓ was first used by the Swiss chemist Sch�nbein in 1838. You mightguess, merely from the etymology of the word, that the field of geochemistry is somehow amarriage of the fields of geology and chemistry. That would be a good guess. But just how are

chemistry and geology combined within geochemistry; what is the relationship between them? Per-haps the best explanation would be to state that in geochemistry, we use the tools of chemistry t osolve geological problems; that is, we use chemistry to understand the Earth and how it works. TheEarth is part of a family of heavenly bodies, our Solar System, that formed simultaneously and areclosely related. Hence, the realm of geochemistry extends beyond the Earth to encompass the entireSolar System. The goals of geochemistry are thus no different from those of other fields of earth sci-ence; just the approach differs. On the other hand, while geochemists have much in common withother chemists, their goals differ in fundamental ways. For example, our goals do not include elu-cidating the nature of chemical bonding or synthesizing new compounds, although these may often beof interest and use in geochemistry. Though geochemistry is a subdiscipline of earth science, it is avery broad topic. So broad in fact that no one can really master it all; geochemists invariablyspecialize in one or a few aspects, such as atmospheric chemistry, geochemical thermodynamics,isotope geochemistry, marine chemistry, trace element geochemistry, soil chemistry, etc.

Geochemistry has flourished in the quantitative approach that has dominated earth science inthe second half of the twentieth century. This quantitative approach has produced greater advancesin the understanding of our planet in the last 50 years than in all of prior human history. The contri-butions of geochemistry to this advance have been simply enormous. Much of what we know abouthow the Earth and the Solar System formed has come from research on the chemistry of meteorites.Through geochemistry, we can quantify the geologic time scale. Through geochemistry, we can de-termine the depths and temperatures of magma chambers. Through geochemistry, mantle plumeswere recognized. Through geochemistry, we know that sediments can be subducted into the mantle.Through geochemistry, we know the temperatures and pressures at which the various metamorphicrock types form and we can us this information, for example, to determine the throw on ancient faults.Through geochemistry, we know how much and how fast mountain belts have risen. Throughgeochemistry, we are learning how fast they are eroding. Through geochemistry, we are learninghow and when the EarthÕs crust formed. Through geochemistry, we are learning when the EarthÕsatmosphere formed and how it has evolved. Through geochemistry, we are learning how the mantleconvects. Through geochemistry, we are learning how cold the ice ages were and what caused them.The evidence of the earliest life, 3.8 gigayears (billion, or 109 years, which we will henceforthabbreviate as Ga), is not fossilized remains, but chemical traces of life. Similarly, the tenuousevidence that life existed on Mars about the same time is also largely chemical. Not surprisingly,instruments for chemical analysis have been key part of probes sent to other heavenly bodies,including Venus, Mars, Jupiter. Geochemistry lies at the heart of environmental science andenvironmental concerns. Problems such as acid rain, the ozone hole, the greenhouse effect and globalwarming, water and soil polution are geochemical problems. Addressing these problems requires aknowledge of geochemistry. Similarly, most of our non-renewable resources, such as metal ores andpetroleum, form through geochemical processes. Locating new sources of these resources increasingrequires geochemical approaches. In summary, every aspect of earth science has been advancedthrough geochemistry.

Though we will rarely discuss it in this book, geochemistry, like much of science, is very muchdriven by technology. Technology has given modern geochemists tools that allow them to study theEarth in ways that pioneers of the field could not have dreamed possible. The electron microprobeallows us to analyze mineral grains on the scale of microns in minutes; the electron microscope allows

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us to view the same minerals on almost the atomic scale. Techniques such as X-ray diffraction, nu-clear magnetic resonance, and Raman and infrared spectroscopy allow us to examine atomic orderingand bonding in natural materials. Mass spectrometers allow us to determine the age of rocks and thetemperature of ancient seas. Ion probes allow us to do these things on micron scale samples. Analyti-cal techniques such as X-ray fluorescence and inductively coupled plasma spectrometry allow us toperform in minutes analyses that would days using ÒclassicalÓ techniques. All this is done withgreater precision and accuracy than was possible just a few decades ago. Mega-computers with mega-hertz of power and megabytes of memory allow us to perform in seconds thermodynamic calculationsthat would have taken years or lifetimes half a century ago; the giga-computers just around the cor-ner will offer us even more power. New instruments and analytical techniques now being developedpromise even greater sensitivity, speed, accuracy, and precision. Together, these advances will bringus ever closer to our goal understanding the Earth and its cosmic environment.

This BookThe intent of this book is to introduce you to geochemistry and to further your understanding of the

Earth through it. To do this, we must first acquire the tools of the trade. Every trade has a set oftools. Carpenters have their saws and T-squares; plumbers have their torches and wrenches.Psychologists have their blot tests, physicians their stethoscopes, accountants their balance sheets,geologists have their hammers, compasses, and maps. Geochemists too have a set of tools. These in-clude not only a variety physical tools such as analytical instruments, but interpretative tools tha tallow them to make sense of the data these instruments produce. The first part of this book, entitledThe Geochemical Toolbox, is intended to familiarize you with the tools of geochemistry. Theseinclude the tools of thermodynamics, kinetics, aquatic chemistry, trace element geochemistry, andisotope geochemistry. Once we have a firm grip on these tools, we can use them to dissect the Earth inthe second part of the book, entitled Understanding the Earth. We begin at the beginning, with theformation of the Earth and the Solar System. We then work our way upward through the Earth,from the mantle and core, through the crust and hydrosphere, and finally into the atmosphere.

In filling our geochemical toolbox, we start with the tools of physical chemistry: thermodynamicsand kinetics. Thermodynamics is perhaps the most fundamental tool of geochemistry; most othertools are build around this one. For this reason, Chapters 2, 3, and 4 are devoted to thermodynamics.Thermodynamics allows us to predict the outcome of chemical reactions under a given set of condi-tions. In geochemistry we can, for example, predict the sequence of minerals that will crystallizefrom a magma under given conditions of temperature and pressure. The mineral assemblage of the re-sulting igneous rock, however, will not be stable at some other temperature and pressure. Thermody-namics allows us to predict the new suite of minerals that replace the original igneous ones. Thusthermodynamics provides enormous predictive power for the petrologist. Since geologists and geo-chemists are more often concerned with understanding the past than with predicting the future, thismight seem to be a pointless academic exercise. However, we can also use thermodynamics in thereverse sense: given a suite of minerals in a rock, we can use thermodynamics to determine thetemperature and pressure conditions under which the rock formed. We can also use it to determine thecomposition of water or magma from which minerals crystallized. This sort of information has beeninvaluable in reaching our understanding of how the Earth has come to its present condition. We canuse this information to determine the amount of uplift experienced by a mountain range, the tempera-ture at which an ore deposit formed, or the composition of ancient seas.

Thermodynamics has an important limitation: it is useful only in equilibrium situations. The rateat which chemical systems achieve equilibrium increases exponentially with temperature. Thermo-dynamics will be most useful at temperatures relevant to the interior of the Earth, say 500¡ C andabove, because equilibrium will be closely approached in most cases. At low temperatures, that is,temperatures relevant to the surface of the Earth, many geochemical systems will not be in equilib-rium and are governed by partly or largely by kinetics, the subject of Chapter 5. Kinetics deals withthe rates and mechanisms of reactions. In this chapter, we will also touch upon such topics as diffu-sion and mineral surfaces. We will see that kinetics is intimately related to thermodynamics.



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In Chapter 6, we see how tools of physical chemistry are adapted for use in dealing with naturalsolutions, the subject of aquatic chemistry. Much of the EarthÕs surface is covered by water, and waterusually is present in pores and fractures to considerable depths even on the continents. This water isnot pure, but is instead a solution formed by interaction with minerals. In Chapter 6, we acquire toolsthat allow us to deal with the interactions among dissolved species, including both amongthemselves and with the solids with which they come in contact. These interactions includephenomena such as dissolution and precipitation, complexation, adsorption and ion exchange. Claysare often the products of water-rock interaction and they have some very interesting chemicalproperties, so we will have a particularly close look at this group of minerals. The tools of aquaticchemistry are essential to understanding processes such as weathering and precipitation ofsedimentary minerals, as well as dealing with environmental problems.

In Chapter 7, we move on to trace element geochemistry. In this chapter we will see that traceelements have provided remarkable insights into the origin and behavior of magmas. Without ques-tion, their value to geochemists far outweighs their abundance. There are several reasons for this.Their concentrations vary much more than do those of the more abundant elements, and their behav-ior tends often to be simpler and easier to treat than that of major elements (a property we will cometo know as HenryÕs Law). Geochemists have developed special tools for dealing with trace elements;the objective of Chapter 7 is to become familiar with them.

Chapters 8 and 9 are devoted to isotope geochemistry. In Chapter 8, we learn that radioactive de-cay adds the important element of time; radioactivity is natureÕs clock. By learning to read thisclock, we now know the age of the Earth and the continents, and we have gained some perspective onthe rate and manner of evolution of the Earth. We can also use the products of radioactive decay,Òradiogenic elementsÓ, as tracers. By following these tracers much as we would dye in fish tank, wecan follow the evolution of a magma, the convection pattern of the mantle, and the circulation of theoceans. The isotopes of another set of elements vary not because of radioactive decay, but because ofsubtle differences in their chemical behavior. These Òstable isotopesÓ are the subject of Chapter 9.The subtle differences in isotopic abundances of elements such as H, C, N, O, and S have, among otherthings, revealed the causes of the ice ages, provided insights into the composition of the ancient a t -mosphere, and reveal the diets of ancient peoples. Stable isotope geochemistry is the last of our geo-chemical tools.

With our toolbox full, we examine the Earth from the geochemical perspective in the second partof the book. We begin in Chapter 10 by looking at Òthe big pictureÓ: the cosmos and the Solar System.We learn how the chemical elements were formed, and how they, in turn, formed our Solar Systemand the Earth. We will find the tools of thermodynamic and isotope geochemistry particularlyvaluable in this Chapter. We will focus particularly closely on meteorites, because the chemistry ofthese objects provides the best record of the early history of the Solar System. Meteorites also pro-vide essential information about the composition of the Earth as a whole, which will in turn be valu-able to us in the following chapter.

In Chapter 11, we begin our inside-out geochemical tour of the Earth. First, we consider the compo-sition of the Earth as a whole, then see how the Earth has differentiated into two major reservoirs:the mantle and core. We pay particular attention to the mantle. Though remote, the mantle ishardly irrelevant. It is important for several reasons. First, it constitutes 1/2 of the mass of theEarth. Second, the reservoirs we are most familiar with, the crust, the hydrosphere, and the atmos-phere, have all formed from the mantle. Third, most geologic processes are ultimately a result ofprocesses occurring within the mantle, processes such as convection and melting. In Chapter 12, we re-turn to more familiar territory: the EarthÕs crust. We will find that geochemistry has provided muchof our knowledge of how the crust has formed and how it has differentiated. We will find the toolsof isotope and trace element geochemistry particularly useful in our examination of the solid Earth.

The next three chapters focus on processes at the surface of the Earth. Here water is the dominantsubstance, and the tools of thermodynamics, kinetics, and aquatic chemistry will be of great use. InChapter 13, we will take a close look at the interaction between water and the EarthÕs surface, andprocesses such as weathering and soil formation. We will see how these processes control the chemis-



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try of streams, rivers, and lakes. Life is also an important force in shaping the face of our planet. Thechemistry of living organisms is part of biochemistry and not geochemistry, so we will treat intracel-lular processes only very briefly. However, organisms produce a vast array of chemicals that findtheir way into the physical environment. In Chapter 14, we will examine the role these organicchemicals play in aquatic chemistry. We will also see how these chemicals are transformed into sub-stances of great geological and societal interest: oil, gas, and coal. Most of the water at the surface ofthe Earth is in the oceans, so we devote Chapter 15 to marine chemistry. We will find that oceansare a fascinating example of an ÒopenÓ geochemical system, with material constantly flowing bothinto and out. We will see that in the face of this constant change, geological and biological processestogether produce a solution with very uniform concentrations of the major species, but highly variableconcentrations of the minor ones.

Before we begin our study of geochemistry, we will devote the remainder of the chapter to review-ing some ÒfundamentalsÓ. First, we briefly examine the philosophy and approach that is common toall science. Then we review the most fundamental aspects of chemistry: how matter is organized intoatoms and how these atoms interact to form compounds. Finally, we review a few fundamental as-pects of the Earth.

The Philosophy of ScienceThis book will concentrate on communicating to you the body of knowledge we call geochemistry.

Geochemistry is just part of a much larger field of human endeavor we call science. Science is cer-tainly among humanityÕs greatest successes; without it, our current civilization would not be possible.Among other things, it would simply not be possible to feed, cloth, and shelter as many people as l ivetoday. This phenomenal success is due in large part to the philosophy of science.

Science consists of two parts: the knowledge it encompasses and the approach or philosophy tha tachieves that knowledge. The goal of all science is to understand the world around us. The arts andhumanities also seek understanding. Science differs from those fields as much by its approach andphilosophy as by its body of knowledge.

A common approach and philosophy unite the great diversity of fields that we collectively callscience. When one compares the methods and tools of a high energy physicist with those of a behav-ioral biologist, for example, it might at first seem that they have little in common. Among otherthings, their vocabularies are sufficiently different that each would have difficulty communicatinghis research to the other. In spite of this, they share at least two things. The first is a criterion ofÒunderstandingÓ. Both the physicist and the behavioral biologist attempt to explain their observa-tions by the application of a set of rules, which, by comparison to the range of phenomena considered,are both few and simple. Both would agree that a phenomenon is understood if and only if the out-come of an experiment related to that phenomenon can be predicted beforehand by applying thoserules to measured variables*. The physicist and biologist also share a common method of seeking un-derstanding, often called the Òscientific methodÓ.

Building Scientific Understanding

Science deals in only two quantities: observations and theories. The most basic of these is the ob-servation. Measurements, data, analyses, experiments, etc. are all observations in the present sense.An observation might be as simple a measurement of the dip and strike of a rock formation or as com-plex as the electromagnetic spectrum of a star. Of course, it is possible to measure both the dip of rockstrata and a stellar spectrum incorrectly. Before an observation becomes part of the body of scientificknowledge, we would like some reassurance that it is right. How can we tell whether observationsare right or not? The most important way to verify an observation is to replicate it independently. In

* Both would admit that chance, or randomness, can affect the outcome of any experiment (though theaffect might be slight). By definition, the effect of this randomness cannot be predicted. Where theeffects of randomness are large, one performs a large collection, or ensemble, of experiments and thenconsiders the average result.



5 August 21, 1997

the strictest sense, ÔindependentÕ means by a separate observer, team of observers, or laboratory, andpreferably by a different technique or instrument. It is not practicable to replicate every observationin this manner, but critical observations, those which appear to be inconsistent with existing theoriesor which test the predictions of newly established ones should be, and generally are, replicated. Buteven replication does not guarantee that an observation is correct.

Observations form the basis of theories. Theories are also called models, hypotheses, etc. Scien-tific understanding is achieved by constructing and modifying theories to explain observations.Theories are merely the products of the imagination of scientists, so we also need a method of sortingout ÔcorrectÕ theories from ÔincorrectÕ ones. Good theories not only explain existing observations, butmake predictions about the outcome of still unperformed experiments or observations. Theories a r etested by performance of these experiments and comparison of the results with the predictions of t h etheory. If the predictions are correct, the theory is accepted and the phenomenon considered to be un-derstood, at least until a new and different test is performed. If the predictions are incorrect, the the-ory is discarded or modified. When trying to explain a newly discovered phenomenon, scientists oftenreject many new theories before finding a satisfactory one. But long-standing theories that success-fully explain a range of phenomena can usually be modified without rejecting them entirely whenthey prove inconsistent with new observations.

Occasionally, new observations are so inconsistent with a well-established theory that it must bediscarded entirely and a new one developed to replace it. Scientific ÔrevolutionsÕ occur when majortheories are discarded in this manner. Rapid progress in understanding generally accompanies theserevolutions. Such was the case in physics in the early 20th century when the quantum and relativitytheories replaced Newtonian theories. The development of Plate Tectonics in the 1960Õs and 1970Õs isan excellent example of a scientific revolution in which old theories were replaced by a single newone. A range of observations including the direction of motion along transform faults, the magneticanomaly pattern on the sea floor, and the distribution of earthquakes and volcanoes were either notpredicted by, or were inconsistent with, classical theories of the Earth. Plate tectonics explained a l lthese and made a number of predictions, such as the age of the seafloor, that could be tested. Thusscientific understanding progresses through an endless cycle of observation, theory construction andmodification, and prediction. In this cycle, theories can achieve ÒacceptanceÓ, but can never beproven correct, because we can never be sure that it will not fail some new, future test.

Quite often, it is possible to explain observations in more than one way. That being the case, weneed a rule that tells us which theory to accept. When this occurs, the principle is that the theorythat explains the greatest range of phenomena in the simplest manner is always preferred. For ex-ample, the motion of the Sun across the sky is quite simple and may be explained equally well by im-aging that the Sun orbits the Earth as visa versa. However, the motions of the planets in the sky arequite complex and require a very complex theory if we assume they orbit the Earth. If we theorizethat the Earth and the other planets all orbit the Sun, the motions of the planets become simple el-liptical orbits and can be explained by NewtonÕs three laws of motion. The geocentric theory waslong ago replaced by the heliocentric theory for precisely this reason. This principle of simplicity, orelegance, also applies to mathematics. Computer programmers call it the KISS (Keep It Simple,Stupid!) Principle. In science, we can sum it up by saying: donÕt make nature any more complex than i talready is.

The Scientist as Skeptic

Though we often refer to Òscientific factsÓ, there are no facts in science. A fact, by definition, can-not be wrong. Both observations and theories can be, and sometimes are, wrong. Of course, some obser-vations (e.g., the Sun rises each morning in the East) and theories (the Earth revolves around the Sun)are so oft repeated and so well established that they are not seriously questioned. But remember tha tthe theory that the Sun revolves around the Earth was itself once so well established that it was notseriously questioned.

One of the ways science differs from other fields of endeavor is that in science nothing is sacred. I tis best to bear in mind the possibility, however remote, that any observation or theory can be wrong.



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Conversely, we must also accept the possibility that even the wildest observations and theoriesmight be correct: in quantum physics, for example, there is a great range of well-replicated observa-tions that can only be labeled as bizarre (see, for example, Gribbin, 1984). ÔIntuitionÕ plays a greaterrole in science that most scientists might be willing to admit, even though scientific intuition is oftenvery useful. Nevertheless, our intuition is based largely on our everyday experience, which is verylimited compared to the range of phenomena that science attempts to understand. As a result, our in-tuition often deceives us. Sometimes we must put it aside entirely. That a clock will run slower if i tmoves faster, or that an electron can behave both as a wave and a particle, or that continents movegreat distances are all very counter-intuitive observations, but all are (apparently) correct. Thusskepticism is one of the keys to good science. In science, never totally believe anything, but never to-tally disbelieve anything either.

Elements, Atoms, and Chemical Bonds: Some Chemical Fundamentals

The Periodic Table

WeÕll begin our very brief review of chemical fundamentals with the Periodic Table. In DmitriMendeleyevÕsà day, chemistry and geochemistry were not as distinct as they are today. Chemistswere still very much occupied with discovering new elements, and they generally sought them in nat-ural materials. For a variety of reasons, therefore, the MendeleyevÕs periodic table provides a goodpoint of departure for us.

MendeleyevÕs periodic table of the elements was the sort of discovery that produces revolutions in

à Dmitri Ivanovich Mendeleyev was born in Tobolsk, Russia in 1834. He became professor of chemistryat St Petersburg in 1866. His periodic table was the sort of discovery that noble prizes are awarded for,but it came before the prize was established. He was honored, however, by having element number 101,medelevium, named for him. Mendeleyev died in 1906.

1 2 3 4 5 6 7 189 11 12 13 14 15 16 178 10

1

2

3

4

5

6

7

(6)

(7)

Group

Rare Earths

Lantanides

Actinides

H He

Li

Na

K

Rb

Cs

Fr

Be

Mg

Ca

Sr

Ba

Ra

Sc

Y

La

Ti

Zr

Hf

V

Nb

Ta

Cr

Mo

W

Mn

Tc

Re

Fe

Ru

Os

Co

Rh

Ir

Ni

Pd

Pt

Cu

Ag

Au

Zn

Cd

Hg

B C N O F Ne

Al Si P S Cl Ar

Ga Ge As Se Br K

In Sn Sb Te I Xe

Tl Pb Bi Po At Rd

La Ce Pr Nd Pm Eu Gd Tb Dy Ho Er Tm Yb Lu

Ac Th Pa U

Ac

Np Pu

Sm

3 4 5 6 7 8 9 10

1 2

11 12 13 14 15 16 17 18

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

37 38 39 40 41 42 43 44 45 46 48 49 50 51 52 53 54

55 56 57 72

59 60 61 62 63 64 65 66 67 68 69 70 7158

73 74 75 76 77 78 79 80 81 82

57

83 84 85 86

87 88 89

89 90 91 92

47

Perio

d

Figure 1.1. The Periodic Table showing element symbols and atomic numbers. Many older periodic ta -bles number the groups as IA-VIIIA and IB-VIIB. This version shows the current IUPAC Convention.



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science. Chemistry had evolved tremendously through the first half of the nineteenth century. Be-tween the publication of LavoisierÔs The Elements of Chemistry, often considered the first moderntext in chemistry, in 1789 and MendeleyevÕs 1869 paper, the number of known elements had increasedfrom 23 to 67. The concepts of the atom and the molecule were well established, and role of electro-magnetic forces in chemical interactions was at least partly understood. Nevertheless, the structureof atoms, and how this structure governed chemical properties of the atom were to be twentieth cen-tury discoveries (though there were some interesting prescient theories). MendeleyevÕs great contri-bution was to show that properties of the elements are a periodic function of atomic weights. Like a l lgood scientific theories, this one made predictions: Mendeleyev was not only able to predict the dis-covery of then unknown elements, such as B, Sc, Ga, and Ge, but also their characteristics and probablemode of discovery. The periodic table led the way not only to the discovery of the remaining ele-ments, but also to understanding the fundamental controls on chemical behavior.

Figure 1.1 shows the periodic table as we know it today. Like most theories, MendeleyevÕs hasgone through some revision since it was first proposed. Most importantly, we now organize the peri-odic table based on Atomic Number rather than atomic weight. The atomic number of an element isits most important property, and is determined by the number of protons in the nucleus (thus the termsatomic number and proton number are synonymous). The number of protons in turn determines both thenumber of electrons and how these electrons are organized.

The mass of an atom is a function of both the proton number and the neutron number, i.e., the numberof neutrons in the nucleus*. Generally, several possible numbers of neutrons can combine with a givennumber of protons to form a stable nucleus (we will discuss nuclear stability in greater detail in Chap-ter 8). This gives rise to different isotopes of the same element, i.e., atoms that have the same atomicnumber but different masses. For example, helium has 2 stable isotopes: 3He and 4He. Both 3He and4He have 2 protons (and a matching number of electrons), but 4He has 2 neutrons while 3He has only 1.

The atomic weight of an element depends on both the masses of its various isotopes and on the rel-ative abundances of these isotopes. This bedeviled nineteenth century chemists. William Prout(1785-1850), an English chemist and physiologist, had noted in 1815 that the densities of a number ofgases were integer multiples of the density of hydrogen (e.g., 14 for nitrogen, 16 for oxygen). This lawappeared to extend to many elemental solids (e.g., 12 for C, 28 for Si) as well, and it seemed reason-able that this might be a universal law. But there were puzzling exceptions. Cl, for example, has anatomic weight of 35.45 times that of hydrogen. The mystery wasnÕt resolved until Thompson demon-strated the existence of 2 isotopes of Ne in 1918. The explanation is that while elements such as H,N, O, C, and Si consist almost entirely of a single isotope, and thus have atomic weights very close tothe mass number of that isotope, natural Cl consists of about 75% 35Cl and 25% 37Clà.

Electrons and Orbits

We stated above that the atomic number of an element is its most important property. This is truebecause the number of electrons is determined by atomic number, as it is the electronic structure of anatom that largely dictates it chemical properties. The organization of the elements in the periodictable reflects this electronic structure.

* The neutron mass and proton mass are almost identical. By convention, the mass number, which is the sum of protons and neutrons in the nucleus, of an isotopeis written as a preceeding superscript. However, for historical reasons, one says ÒheliumÐ4Ó. Note alsothat the atomic number or proton number can be readily deduced from the chemical symbol (atomicnumber of He is 2). The neutron number can be found by subtracting the proton number from the massnumber. Thus the symbol Ô4HeÕ gives a complete description of the nucleus of this atom.à The actual mass of a atom depends on the number of electrons and the nuclear binding energy as well asthe number of protons and neutrons. However, the mass of the electron is over 1000 times less than themass of the proton and neutron, which are about equal, and the effect of nuclear binding energy on masswas too small for 19th century chemists to detect.



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The electronic structure of atoms, and indeed the entire organization of the periodic table, is de-termined by quantum mechanics and the quantization of energy, angular momentum, magnetic moment,and spin of electrons. Four quantum numbers, called the principal, azimuthal, magnetic, and spinquantum numbers and conventionally labeled n, l, m, and ms, control the properties of electrons associ-ated with atoms. The first of these, n, which may take values 1, 2, 3, ..., determines most of the elec-tronÕs energy as well as mean distance from the nucleus. The second, l, which has values 0, 1, 2, ... n-1,determines the total angular momentum and the shape of the orbit. The third, m, which may havevalues -l, ...0...l, determines the z component of angular momentum and therefore the orientation ofthe orbit. The fourth, ms, may have values of Ð1/2 or +1/2 and determines the electronÕs spin. The firstthree quantum numbers result in the electrons surrounding the nucleus being organized into shells , sub-shells , and orbitals*. The Pauli Exclusion Principle requires that no two electrons in an atom mayhave identical values of all four quantum numbers. Because each orbital corresponds to a unique set ofthe first 3 quantum numbers, only 2 electrons may occupy a given orbital, and then only if they havedifferent spins. In Chapter 8 we will see that the properties of the nucleus are also dictated by quan-tum mechanics, and that the nucleus may also be thought of as having a shell structure.

Each shell corresponds to a different value of the principal quantum number. The periodic natureof chemical properties reflects the filling of successive shells as additional electrons (and protons)are added. Each shell corresponds to a ÔperiodÕ, or row, in the periodic table. The first shell (the Kshell) has one subshell, the 1s, consisting of a single orbital (with quantum numbers n=1, l=0, m=0.The 1s orbital accepts up to 2 electrons. Thus period 1 has 2 elements: H and He. If another electronand proton are added, the electron is added to the first orbital, 2s, of the next shell (the L shell).Such a configuration has the chemical properties of Li, the first element of period 2. The second shellhas 2 subshells, 2s (correspondingto l=0) and 2p (corresponding tol=1). The p subshell has 3 orbitals(which correspond to values for mof -1, +1, and 0), px, py, and pz, sothe L shell can accept up to 8 elec-trons. Thus period 2 has 8 ele-ments.

There are some complexities inthe filling of orbitals beyond the Lshell. In the M shell, which corre-sponds to period 3, there is thepossibility of putting electrons inthe d subshell (l=2), but this is en-ergetically less favorable thanelectrons going in the subsequentshell. Thus the 3d subshell is va-cant in period 3 element in theirground states, and in the first 2elements of period 4. Only whenthe 4s orbital is filled do electronsbegin to fill the 3d orbitals. The 5

* It is often convenient to think of the electrons orbiting the nucleus much as the planets orbit the Sun.This analogy has its limitations. The electronÕs position can not be precisely specified as can a planetÕs.In quantum mechanics, the Schr�dinger Wave function, ψ (or more precisely, ψ2) determines theprobability of the electron being located in a given region about the atom. As an example of failure ofthe classical physical description of the atom, consider an electron in the 1s orbital. Both quantumnumber specifying angular momentum, l and m, are equal to 0, and hence the electron has 0 angularmomentum, and hence can not be in an orbit in the classical sense.

1s

2s

3s

4s

5s

6s

7s

2p

3p

4p

5p

6p

7p

3d

4d

4d

6d 5f

4f

No. of electrons

(2)

(8)

(8)

(18)

(18)

(32)

(32)Period

1

2

3

4

5

6

7

Energ

y

Figure 1.2. The predicted sequence of orbital energies for elec-trons in atoms. S levels can hold 2 electrons, p, d, and f can hold6, 10, and 14 respectively.



9 August 21, 1997

3d orbitals are filled as one passes up the first transition series metals, Sc through Zn. This results insome interesting chemical properties, which we will consider in Chapter 7. Similarly, the secondand third transition series metals correspond to filling of the 4d and 5d orbitals. The Lanthanide andActinide rare earth elements correspond to the filling of the 4f and 5f shells are filled (again result-ing in some interesting properties, which we will consider subsequently). The predicted sequence inwhich orbitals are filled and their energy levels are shown in Figure 1.2. Figure 1.3 shows the elec-tronic configuration of the elements.

Finding the Electron: Atomic Structure and the Schrödinger EquationThe modern atomic theory of matter was first proposed by Dalton at the beginning of the 19th cen-

tury, but it was not until the beginning of the 20th century that the structure atoms began to be re-vealed. In 1910 Ernest Rutherford proposed, based on α -particle scattering experiments, that atomsconsisted of dense, small, positively charged nuclei surrounded by orbiting elections. Three yearslater, Niels Bohr introduced some aspects of the new quantum theory into the description of electronorbits. He was able to predict successfully the energy of the electron in the orbit of the hydrogen atomand thus to explain the electromagnetic emission spectrum of hydrogen. But the Bohr theory failed todescribe the spectra of more complex atoms. A more satisfactory description of the electronic structureof atoms was not made until Erwin Schr�dinger and Werner Heisenberg, building on a theory of Louisde Broglie, developed a fully quantum mechanical theory in 1926.

Quantum mechanics treats the electron as a wave. Any wave, be it a displacement wave on a tautstring or an electromagnetic wave, traveling in direction x must satisfy the wave equation:

∂2F

∂x2

=1

ω2

∂2F

∂t2

1.1

where F is the wave function (for example, the displacement of the string from equilibrium or theelectric or magnetic field), and ω is the wavespeed. For an electron bound to an atom, it can be shownthat this becomes (in 1 dimensional space):

1s 1

2s 1 2s 2 2s 22p 1

1s 2

2s 22p 2 2s 22p 3 2s 22p 4 2s 22p 4 2s 22p 6

3s 1 3s 2 3s 23p 1 3s 23p 2 3s 23p 3 3s 23p 4 3s 23p 4 3s 23p 6

4s 1 4s 2 4s 24p 1 4s 24p 2 4s 24p 3 4s 24p 4 4s 24p 4 4s 24p 64s 23d 104s 23d 1 4s 23d 2 4s 23d 3 4s 23d 4 4s 23d 5 4s 23d 6 4s 23d 7 4s 23d 8 4s 23d 9



6s 24f116s 24f3 6s 24f4 6s 24f5 6s 24f6 6s 24f7 6s 24f9 6s 24f106s 25d 1 6s 24f146s 24f12 6s 24f13

7s 26d 27s 26d 1

7s 26d 17s 1 7s 2

7s 5f 627s 6d 5f 22 1 7s 6d 5f 32 1 7s 6d 5f 42 1

6s 5d 4f 72 1 6s 5d4f 142 16s 5d 4f12 1

H He

Li

Na

K

Rb

Cs

Fr

Be

Mg

Ca

Sr

Ba

Ra

Sc

Y

La

Ti

Zr

Hf

V

Nb

Ta

Cr

Mo

W

Mn

Tc

Re

Fe

Ru

Os

Co

Rh

Ir

Ni

Pd

Pt

Cu

Ag

Au

Zn

Cd

Hg

B C N O F Ne

Al Si P S Cl Ar

Ga Ge As Se Br K

In Sn Sb Te I Xe

Tl Pb Bi Po At Rd


Ac Th Pa U

Ac

Np Pu

Sm

Figure 1.3. The Periodic Table showing the electronic configuration of the elements. Only the lastorbitals filled are shown, thus each element has electrons in the orbitals of all previous group 18elements (noble gases) in addition to those shown. Superscripts indicate the number of electrons ineach subshell.



10 August 21, 1997

h2

8π2m

d2Ψ

dx2

+ (E – V)Ψ = 0 1.2

where h is PlanckÕs constant, m is the mass of the electron, E is its kinetic energy, Ψ is the electronÕswave function, and V is the potential energy: V= Ze2/r (e is the charge of the electron, r is the dis-tance of the electron from the nucleus, and Z is the atomic, or proton, number and is 1 for hydrogen).Equation 1.2 is known as the Schr�dinger Equation. What is the significance of the wave function Ψ?This question puzzled even Schr�dinger, who suggested it was related to charge density. The correctanswer was provided by Max Born shortly after publication of Schr�dingerÕs paper, who proposedthat it was related to the probability of finding the electron. Specifically, Born suggested that theprobability of finding the electron, P, in a given interval dx at time t was given by:

P = Ψ(x, t)2 dx 1.3 Ψ is sometimes called the probability amplitude.

The full (non-relativistic, time-independent) Schr�dinger equation for 3-dimensional space is: h2

2m

∂2Ψ

∂x2

+∂

2Ψ

∂y2

+∂2Ψ

∂z2

+ (E – V)Ψ = 0 1.4

where hÑ = h/2¹; h is PlanckÕs constant. In general, however, it is more convenient to write it inspherical coordinates:

1

r2

∂

∂rr2 ∂ψ

∂r+

1

r2sin θ

∂

∂θsin θ

∂ψ

∂θ+

1

r2sin2 θ

∂2ψ

∂φ2

h2

2m+ E – V ψ = 0 1.5

where x = r sin θ cos φ, y = r sin θ sin φ, and z = r cos θ. A sketch of the spherical coordinate system isshown in Figure 1.4.

The problem now becomes one of ÔguessingÕ functions for E and Ψ(r, θ, φ) that satisfy equation 1.3.This task can be simplified if we use our physical and mathematical knowledge to constrain ourguesses. As a first step, we can recall that the Bohr model successfully explains the electromagneticemission spectrum of the hydrogen atom, so we might adopt a value for E for hydrogen matching tha tof the Bohr model. We can also expect that energy levels will be quantized, so an integer quantum en-ergy number, n, should enter somewhere. Indeed, work in the 19th century had already suggested tha tn should occur in the energy expression as an inverse square term. Thus we might guess at that the en-ergy term will be:

E=

me4

2h2n

2=

e2

n2

2r0

1.6

where r0 is the Bohr radius (r0 = 0.529 �, where � is �ngstroms, 10-8 cm). What about Ψ? As a first guess, we might try a spherically symmetric solution, i.e., one in which

the ¶Ψ/¶θ and ¶Ψ/¶φ terms are 0. This will clearly simplify equation 1.3. An electron bound to a hy-drogen atom is unlikely to be found at great distance from the nucleus, so Ψ should go to 0 for large r.Thus we might try a solution of the form Ψ(r) = aeÐbr, where a and b are constants. Setting n = 1 inequation 1.6, we find a solution when a = (1/π)1/2(1/r0)3/2 and b = 1/r0. Thus:

ψ(r) =

1

π1/2

1

r0

3/2

e–r/r0 1.7

As it turns out, there is a whole family of spherically symmetric solutions that may be obtained bysetting n = 1, 2, 3, ...; for example, for n = 2,



11 August 21, 1997

ψ(r) =

1

4 2π1/2

1

r0

3/2

2 –r

r0e

–r/r0 1.8

z

x

y

3d xy

z

y

x

z

y

x

2pz

z

y

x

θφ

z

y

x

1s

3d z 2

Figure 1.4. Spherical coordinates and 3 dimensional plots of probability density for the 1s, 2pz, 3dxy,and 3dz2 orbitals of hydrogen.

Solutions of this form are designated Ψ1s, Ψ2s, etc., where the s indicates a spherically symmetric so-lutionà and the 1, 2, etc., are the principal quantum numbers.

What will such an orbital Ôlook likeÕ? The orbital is independent of θ and φ and will thereforehave spherical symmetry, as in Figure 1.4. Figure 1.5a shows Ψ plotted versus radial distance fromthe nucleus. The probability of finding the electron in spherical shell of radius r and thickness, dr, isgiven by 4¹r2Ψ2 dr. Figure 1.5b shows the probability function P = 4¹r2Ψ2 plotted against radial dis-tance. In Figure 1.5a, we see that the probability amplitude is highest close to the nucleus, but thevolume of a spherical shell is small, so the probability is low. Far away from the nucleus, the vol-ume of a shell is large, but Ψ is small, so P is also small. Reassuringly, the maximum of P occurs a t

à Actually, the letters s, p, d, f are originally of spectroscopic origin and stood for sharp, principal,diffuse, and fundamental.



12 August 21, 1997

r=r0, the Bohr radius. Thus the Schr�dinger Equation predicts that an electron in the 1s orbital wil lmost likely be found at the Bohr radius.

0

2 4 6 8

Ψ

1

2

3

r, Bohr radii

1s

2s

1s

2s

0.5

0.25

r, Bohr radii

P

2 4 6 8 10

a b

Figure 1.5. Plot of (a) Ψ (r) and (b) P = 4¹r2Ψ2 versus radial distance from the nucleus for the 1s and 2sorbitals. Scale for Ψ is arbitrary. Scale for P is normalized such that the probability of finding theelectron somewhere is 1.

Table 1.1. Quantum numbers and Example solutions to the Schrödinger Equation

orbital n l m Ψ1s 1 0 0

2s 2 0 0

2pz 2 1 0

2px 2 1 -1

2py 2 1 +1

3dz2 3 2 0

3dxy 3 2 -1

1π1/2

1r0

3/2e–r/r0

14 2π 1/2

1r0

3/22 – r

r0e–r/r0

14 2π 1/2

1r0

3/22 – r

r0e–r/r0 cos θ

14 2π 1/2

1r0

3/22 – r

r0e–r/r0sinθ sinφ

14 2π 1/2

1r0

3/22 – r

r0e–r/r0 sinθ cosφ

181 2π 1/2

1r0

3/2 rr0

2e–r/3r0 3cos2θ – 1

181 2π 1/2

1r0

3/2 rr0

2e–r/3r0sinθ cosθ sinφ

Now letÕs look for non-spherically symmetric solutions. First consider the energy term. The s orbi-tals, being spherically symmetric, have no angular momentum. In the general case, there will be somecontribution from the angular momentum to the energy. We need to modify our energy term to take ac-count of this. Perhaps it should come as no surprise that angular momentum is also quantized. Possi-ble angular momentum values are given by:

L = l(l + 1)h2 1.9

where l is an integer between 0 and n-1. Thus nonsymmetric solutions are only possible for n > 1. Theangular momentum contribution to energy is:



13 August 21, 1997

EL =

l(l + 1)h2

2mr2

1.10

As a first guess as to the form of Ψ, one might try a form of the exponential expression for the symmet-ric case. For example:

ψ = x ⋅ ae-br 1.11

It turns out that this and the equivalent y and z forms are solutions. A third quantum number, m, de-termines the orientation of the angular momentum. m may take values Ðl ... +l. Table 1.1 summarizessolutions to the Schr�dinger Equation in terms of the 3 quantum numbers, n, l, and m. Figure 1.4 gives afew examples of the appearance of these orbitals.

Though the Schr�dinger equation and electronic structure ultimately govern virtually all chemicalinteractions, much of geochemistry concerns itself with phenomena on a scale where these detailsneed not be considered. However, as geochemists construct increasingly exact and detailed models,the Schr�dinger Equation comes increasingly into play. We will see an example in chapter 6 how thegeometry of the 3d orbitals plays an important role in governing the geochemical behavior of thefirst transition series metals.

Some Chemical Properties of the Elements

It is only the most loosely bound electrons, those in the outermost shells, that participate in chem-ical bonding, so elements sharing a similar outermost electronic configuration tend to behave simi-

20

10

15

5

Vol

ts

Kr

He

Ne

Ar

Xe

Rn

F

Cl

Br

I

At

O

S

Se

Te

Po

N

P

As

Sb

Bi

Ge

Sn

Pb

Tl

Zn

CdHgCu

AgAu

Ni

Pd

PtCo

RhIr

Fe

Ru

OsMn

ReCr

Mo

W U

VNb

TaPa

Ti

Zr

Hf

Th

C

Si

Al

Sc

Y

LaAc

BBe

Mg

Sr

Ba

Ra

Ca

H

Li

Na

K

Rb

Cs

Fr

FIRST IONIZATIONPOTENTIAL

Figure 1.6. First ionization potential of the elements.



14 August 21, 1997

larly. Elements within the same column, or group, share outer electronic configurations and hence be-have in a similar manner. Thus the elements of group 1, the alkalis, all have 1 electron in the outer-most s orbital, and behave in a similar manner. The group 18 elements, the noble, or rare, gases, a l lhave a filled p subshell, and behave similarly.

LetÕs now consider several concepts that are useful in describing the behavior of atoms and ele-ments: ionization potential, electron affinity, and electronegativity. The First Ionization Potentialof an atom is the energy required to remove (i.e., move an infinite distance away) the least tightlybound electron. This is energy absorbed by the electron in reactions such as:

Na → Na+ + e– 1.12The Second Ionization Potential is the energy required to remove a second electron, etc. The first ion-ization potential of the elements is illustrated in Figure 1.6.

The electron affinity is the energy given up in reactions such as:

F + e– → F– 1.13Electronegativity is another parameter that is often used to characterize the behavior of the ele-

ments. It is a relative, unitless quantity determined from the differences in bond energy between an A-B molecule and the mean energies of A-A and B-B molecules. Electronegativity quantifies the ten-dency of an element to attract a shared electron when bonded to another element. For example, F hasa higher electronegativity than H (the values are 3.8 and 2.5 respectively), thus the bonding electronin hydrogen fluoride, HF, is more likely to be found in the vicinity of F than of H. It is also useful incharacterizing the nature of chemical bonds between elements, as we shall see in a subsequent section.Electronegativities of the elements are shown in Figure 1.7.

In general, first ionization potential, electron affinity, and electronegativities, increase from leftto right across the periodic table, and to a less degree from bottom to top. This reflects the shieldingof outer electrons, particularly those in s orbitals, by inner electrons, particularly those in p orbitals,from the charge of the nucleus. Thus the outer 3s electron of neutral sodium is effectively shieldedfrom the nucleus and is quite easily removed. On the other hand, the 2p orbitals of oxygen are notvery effectively shielded, and it readily accepts 2 additional electrons. With the addition of these2 electrons, the 2p orbital is filled and the 3s orbital effectively shielded, so there is no tendency toadd a third electron. With the outer p (and s) orbitals filled, a particularly stable configuration is

H He

Li

Na

K

Rb

Cs

Fr

Be

Mg

Ca

Sr

Ba

Ra

Sc

Y

La

Ti

Zr

Hf

V

Nb

Ta

Cr

Mo

W

Mn

Tc

Re

Fe

Ru

Os

Co

Rh

Ir

Ni

Pd

Pt

Cu

Ag

Au

Zn

Cd

Hg

B C N O F Ne

Al Si P S Cl Ar

Ga Ge As Se Br K

In Sn Sb Te I Xe

Tl Pb Bi Po At Rd


Ac Th Pa U

Ac

Np Pu

Sm

2.1

1.0

0.9

0.8

0.8

0.7

0.7

1.5

1.2

1.0

1.0

0.9

0.9

1.3

1.2

1.0

1.5

1.4

1.3

1.6

1.6

1.5

1.6

1.8

1.7

1.5 1.8 1.9 1.9 1.9 1.6 1.6 1.8 2.0 2.5 2.8

2.0 2.5 3.0 3.5 4.0

1.5 1.8 2.1 2.5 3.0

1.9 2.2 2.2 2.2

2.22.22.2 2.22.2

1.9 1.7 1.7 1.8 1.9 2.1 2.5

1.9 2.4 1.9 1.8 1.9 1.9

1.21.0

1.31.1

1.0 1.0 1.0 1.0 1.0 1.1 1.1 1.1 1.1 1.1 1.1 1.2 1.2

1.4 1.4 1.4 1.4

1.1

Figure 1.7. Electronegativities of the elements.



15 August 21, 1997

reached. Thus Ne has little tendency to either add or give up an electron.The number of electrons that an element will either give up or accept is known as its valence. For

elements in the ÔwingsÕ of the periodic table (i.e., all except the transition metals), valence is easilydetermined simply by counting how far the element is horizontally displaced from Group 18 in theperiodic table. For Group 18, this is 0, so these elements, the noble gases, have 0 valence. For group 1it is 1, so these elements have valence of +1; for group 17 it is -1, so these elements have valence of -1,etc. Valence of the transition metals is not so simply determined, and these elements can have morethan 1 valence state. Most, however, have valence of 2 or 3, though some, such as U, can have va-lences as high as 6.

A final characteristic that is important in controlling chemical properties is ionic radius. This isdeduced from bond length when the atom is bonded to one or more other atoms. Positively charged a t -oms, or cations, have smaller ionic radii than do negatively charged atoms, or anions. Also, ionic ra-dius decreases as charge increases. This decrease is due both to loss of electrons and to shrinking ofthe orbits of the remaining electrons. The latter occurs because the charge of the nucleus is shared byfewer electrons and hence has a greater attractive force on each. In addition, ionic radius increasesdownward in each group in the periodic table, both because of addition of electrons to outer shells andbecause these outer electrons are increasingly shielded from the nuclear charge by the inner ones.Ionic radius is important in determining important geochemical properties such substitution in solids,solubility, and diffusion rates. Large ions need to be surrounded, or coordinated, by a greater number ofoppositely charged ions than do smaller ones. The ionic radii of the elements are illustrated in Fig-ure 1.8.

We can now summarize a few of the more important chemical properties of the various groups inthe periodic table. Group 18, does not participate in chemical bonding in nature, hence the term ÔnoblegasesÕ. Group 1 elements, the alkalis, readily accept an electron (they are electropositive) and henceare highly reactive. They tend to form ionic bonds rather than covalent ones and hence tend not toform bonds that are as strong as other elements. They tend to be quite soluble in aqueous solutions. Be-cause they have only a +1 charge, their ionic radii tend to be larger than other cations. Group 2 ele-ments, the alkaline earths, have these same characteristics, but somewhat moderated. Group 17 ele-ments, the halogens, are highly electronegative and readily accept an electron, are highly reactive,form ionic bonds, and are quite soluble. Their ionic radii tend to be larger than more highly chargedanions. Elements of Groups 13-16 tend to form bonds that are predominantly covalent. As a result,they tend to be less reactive and less soluble (except where they form soluble radicals, such as SO 4

2–)than Group 1, 2, and 17 elements. Finally, the transition metals are a varied lot. Many form strongbonds (generally with O in nature) and are fairly insoluble, particularly the highly charged ones.

As

At 7+6+PoBi5+

TlHg

SbSnIn3+

Cd2+

Ag1+

Au

Ge4+Ga

3+Zn

2+Cu1+

Li

K

Rb

Cs

Fr

Be

Ca

Sr

Ba

Ra

BAl

Sc

Y

La

Ac

C4+

Si

Ti

Zr

Hf

Th

1+

1+

1+

1+

1+ 2+

2+

2+

2+

2+ 3+

3+

3+

3+

3+

3+4+

4+

4+

4+

4+

Nb

Pa U

Cr Mn

Tc

Os6+

Ru

Co

Ir

Rh3+

Ni

PtPd

W

V 3+

Ta

Mo5+

5+ Re

4+ 4+

4+

4+

3+ 4+Fe 2+

4+

4+

4+

2+ 2+

4+

4+

Pb

NP

O F

Te 2-

Br1-

I 1-

Cl1-

5+

5+

2- 1-

Ionic Radii

5+

1+

2+2+

4+ 5+

3+

S 2-

Se 2-Mg2+Na1+

Figure 1.8. Ionic radii of the elements.



16 August 21, 1997

Some, the Ônoble metalsÕ (Ru, Rh, Pd, Os, Ir, Pt) in particular, tend to be very unreactive and insoluble.The rare earths are of interest because all have 2 electrons in the 6s outer orbital, and vary only bythe number of electrons in the 4fÊshell. Their bonding behavior is thus quite similar. They vary sys-tematically in ionic radius, which makes them of great geochemical interest.

Chemical Bonding

Covalent, Ionic, and Metal Bonds

Except for the noble gases, atoms rarely exist independently: they are generally bound to other a t -oms in molecules, crystals, or ionic radicals. Atoms bind to one another through transfer or sharing ofelectrons, or through electrostatic forces arising from uneven distribution of charge in atoms and mole-cules. A bond that results from the total transfer of electrons from one atom to another is known as anIonic Bond. A good example is the bond between Na and Cl in a halite crystal. In this case, the N aatom (the electropositive element) gives up an electron, becoming positively charged, to the Cl atom(the electronegative element), which becomes negatively charged. Electrostatic forces between theNa+ and the Cl- ions hold the ions in place in the crystal. When electrons are shared between atoms,such as in the H2O molecule or the SiO 4

4– radical, the bond in known as covalent. In a Covalent Bond,the outer electrons of the atoms involved are in hybrid orbits that encompass both atoms.

The ideal covalent and ionic bonds represent the extremes of a spectrum: most bonds are neitherwholly covalent nor wholly ionic. In these intermediate cases, the bonding electrons will spend most,but not all, of their time associated with one atom or another. Electronegativity is useful in describ-ing the degree of ionicity of a bond. Though there is no clear distinction between a covalent and ionicbond, a bond is considered ionic when the difference in the electronegativity of the two atoms in-volved is greater than 2. In Figure 1.7, we see that metals (generally those elements on the left handside of the periodic table) tend to have low electronegativities while the non-metals (those elementson the right) have high electronegativities. Thus bonds between metals and non-metals (e.g., NaCl)will be ionic while those between non-metals (e.g., CO2) will be covalent, as will bonds between twolike atoms (e.g., O2).

Another type of bond occurs in pure metal and metal alloy solids. In the metallic bond, valenceelectrons are not associated with any single atom or pair of atoms; rather they are mobile and may befound at any site in the crystal lattice. Since metals rarely occur naturally (iron meteorites and theEarthÕs core are notable exceptions), this type of bond is less important in geochemistry than otherbonds.

Ionically bonded compounds tend to be good conductors of heat and electricity and have high melt-ing temperatures. They also tend to be hard, brittle and highly soluble in water. Covalently bondedcompounds tend to be good conductors of heat, but not of electricity. They are typically harder andless brittle than ionic solids but less soluble. In molecular solids, such as ice, atoms within the mole-cule are covalently bonded. The molecules themselves, which occupy the lattice points of the crystal,are bonded to each other through van der Waals and/or hydrogen bonds. Such solids are compara-tively weak and soft and generally have low melting points.

Molecules in which electrons are unequally shared have an asymmetric distribution of charge andare termed polar. A good example is the hydrogen chloride molecule. The difference in electronega-tivity between hydrogen and chlorine is 0.9, so we can predict that bonding electron will be shared,but associated more with the Cl atom than with the H atoms in HCl. Thus the H atom will have apartial positive charge, and the Cl atom a partial negative charge. Such a molecule is said to be adipole. The dipole moment, which is the product of one of the charges (the two charges are equal andopposite) times the distance between the charges, is a measure of the asymmetric distribution ofcharge. Dipole moment is usually expressed in debye units (1 debye = 3.3356 × 10Ð34 coloumb-meters).

Van der Waals Interactions and Hydrogen Bonds

Covalent and ionic bonds account for the majority of bonds between atoms in molecules and crystals.There are two other interactions that play a lesser role in interactions between atoms and molecules,



17 August 22, 1997

van der Waals interactions and hydrogen bonds.These are much weaker but nevertheless playan important role in chemical interactions, par-ticularly where water and organic substancesare involved.

Van der Waals interactions arise fromasymmetric distribution of charge in moleculesand crystals. There are three sources for van derWaals interactions: dipole-dipole attraction,induction, and London dispersion forces. As wenoted above, many molecules, including water,have permanent dipole moments. When two po-lar molecules encounter each other, they willbehave much as two bar magnets: they will tendto orient themselves so that the positive part ofone molecule is closest to the negative part ofanother (Figure 1.9a). This results in a net a t -tractive force between the two molecules. Whenthe distance between molecules is large com-pared to the distance between charges within

molecules, the energy of attraction can be shown to be:

UD–D = –23

µ4

r61

k T1.14

where UD-D is the interaction energy, µ is the dipole moment, T is temperature (absolute, or thermo-dynamic temperature, which we will introduce in the next chapter), k is a constant (BoltzmannÕs con-stant, which we shall also meet in the next chapter), and r is distance. We donÕt want to get lost inequations at this point; however, we can infer several important things about dipole-dipole interac-tions just from a quick glance at it. First, the interaction energy depends inversely on the sixth powerof distance. Many important forces, such as electromagnetic and gravitational forces, depend on the

inverse square of dis-tance. Thus we may in-fer that dipole-dipoleforces become weakerwith distance very rap-idly. Indeed, they arelikely to be negligibleunless the molecules arevery close. Second, theinteraction energy de-pends on the forthpower of the dipole mo-ment, so that small dif-ferences in dipole mo-ment will result in largedifferences in interac-tion energy. For exam-ple, the dipole momentof water (1.84 debyes) isless than twice that ofHCl (1.03 debyes), yetthe dipole interaction

b. The Induction Effect

+–

+–

b. Dipole Interaction

++

–

++–

–

–

+

–+++

– ––

Figure 1.9. Van der Waals interactions arisebecause of the polar nature of some molecules.Illustrated here are (a) dipole-dipoleinteractions, which occur when two dipolarmolecules orient themselves so oppositely chargedsides are closest, and (b) the induction effect,which arise when the electron orbits of onemolecule are perturbed by the electromagneticfield of another molecule.

δ−δ−

δ−

δ−δ−δ−

δ+

δ+

δ+

δ+

δ+

δ+Hydrogen bonds

1.7 Å

1.0 Å

Figure 1.10. Hydrogen bonding between water molecules. Hydogenpositions shown as red; sp3 hybrid orbitals in oxygen shown as dark gray.The δ+ and δÐ indicate partial positive and negative chargesrespectively.



18 August 22, 1997

energy between two water molecules (716 J/mol) is nearly 10 times as great as that between two HClmolecules (72.24 J/mol) at the same temperature and distance (298 K and 5�). Finally, we see tha tdipole interaction energy will decrease with temperature.

Dipole molecules may also polarize electrons in a neighboring molecule and distort their orbits insuch a way that their interaction with the dipole of the first molecule is attractive. This is known asthe induction effect (Figure 1.9b). The induction energy also depends on the inverse sixth power of in-termolecular distance, but only on the square of the dipole moment of the molecules involved. In ad-dition, another parameter, the polarizability of a molecule, is also needed to describe this effect. Ingeneral, the attraction arising from induction is less important than from dipole-dipole interaction.However, because it depends only on the square of dipole moment, the induction attraction can belarger than the dipole-dipole attraction for some weakly dipolar molecules. Finally, van der Waals forces can also occur as a result from fluctuations of charge distribution onmolecules that occur on time scales of 10-16 seconds. These are known as London dispersion forces. Theyarise when the instantaneous dipole of one molecule induces a dipole in a neighboring molecule. Aswas the case in induction, the molecules will orient themselves so that the net forces between themare attractive.

The total energy of all three types of van der Waals interactions between water molecules is about380 J/mol assuming an intermolecular distance of 5 � and a temperature of 298 K (25¡ C). Though someinteraction energies can be much stronger (e.g., CCl4, 2.8 kJ/mol) or weaker ( 1 J/mol for He), an energyof a few hundred Joules per mole is typical of many substances. By comparison, the hydrogen-oxygenbond energy for each HÑO bond in the water molecule is 46.5 kJ/mol. Thus van der Waals interac-tions are quite weak compared with typical intramolecular bond energies.

The HydrogenÊBond is similar to van der Waals interactions in that it arises from nonsymmetricdistribution of charge in molecules. However, it differs from van der Waals interactions in a numberof ways. First, it occurs exclusively between hydrogen and strongly electronegative atoms, namelyoxygen, nitrogen and fluorine. Second, it can be several orders of magnitude stronger than van derWaals interactions, though still weak by comparison to covalent and ionic bonds. The exact nature ofhydrogen bonds is not completely understood. They arise principally from electrostatic interactions.In the water molecule, binding between oxygen and hydrogen results in hybridization of s and p orbi-tals to yield two bonding orbitals between the O and two H atoms and 2 non-binding sp3 orbitals on theoxygen. The latter are prominent on the opposite side of the O from the hydrogens. The hydrogen inone water molecule, carrying a net positive charge, is attracted by the non-binding sp3 electrons of theoxygen of another water molecule, forming a hydrogen bond with it (Figure 1.10).

Hydrogen bonds typically have energies in the range of 20-40 kJ/mol. These are much higher thanexpected for electrostatic interactions alone and indeed approach values similar to intramolecularbond energies. Thus there is the suspicion that the some degree of covalency is also involved in thehydrogen bond. That is to say that the non-binding electrons of oxygen are to some degree shared bywith the hydrogen in another molecule. Hydrogen bonds are perhaps most important in water, wherethey account for some of the extremely usual properties of this compound, such as its high heat of va-porization, but they can also be important in organic molecules and are present in HF and ammonia aswell.

A Brief Look at the Earth

Structure of the Earth

The Earth consists of 3 principal layers: the core, the mantle, and the crust (Figure 1.11). The core,roughly 3400 km thick and extending about half way to the surface, consists of Fe-Ni alloy and can besubdivided into an inner and outer core. The outer core is liquid while the inner core is solid. The man-tle is about 3000 km thick and accounts for about 2/3 the mass of the Earth; the core accounting for theother 1/3. The crust is quite thin by comparison, nowhere thicker than 100 km and usually much thin-ner. Its mass is only about 0.5% of the mass of the Earth. There are 2 fundamental kinds of crust: oce-



19 August 22, 1997

anic and continental. Ocean crust is thin(about 6 km) and is nowhere older thanabout 200 million years. The continentalcrust is thicker (about 35-40 km thick onaverage) and relatively permanent.

Both the crust and the mantle consistprincipally of silicates. The mantle iscomparatively rich in iron and magne-sium, so ferromagnesian silicates, such asolivine and pyroxenes, dominate. Rockshaving these compositional characteris-tics are sometimes called ultramafic.The continental crust is poor in iron andmagnesium, and aluminosilicates such asfeldspars dominate. Rocks of this compo-sition are sometimes referred to as felsic.The oceanic crust is intermediate in com-position between the mantle and conti-nental crust and has a mafic composition,consisting of a roughly 50-50 mix of ferro-magnesian minerals and feldspar. Thesedifferences in composition lead to differ-ences in density, which are ultimatelyresponsible for the layering of the Earth,the density of each layer decreasing out-ward. The continental crust is the leastof dense of these layers. The fundamen-

tal reason why continents stick out above the oceans is that continental crust is less dense than oceaniccrust.

Plate Tectonics and the Hydrologic Cycle

Two sources of energy drive all geologic processes: solar energy and the EarthÕs internal heat. So-lar energy drives atmospheric and oceanic circulation, and with them, the hydrologic cycle. In thehydrologic cycle, water vapor in the atmosphere precipitates on the land as rain or snow, percolatesinto the soil and, through the action of gravity, makes it way to the oceans. From the oceans, it isevaporated into the atmosphere again and the cycle continues. The hydrologic cycle is responsiblefor two very important geologic processes: weathering and erosion. Weathering, a topic we will con-sider in more detail in Chapter 13, causes rocks to breakdown into small particles and dissolved com-ponents. The particles and dissolved matter are carried by the flow of water (and more rarely bywind and ice) from high elevation to areas of low elevation. Thus the effect of the hydrologic cycleis to level the surface of the planet.

The EarthÕs internal heat is responsible for tectonic processes, which tend to deform the surface ofthe planet, producing topographic highs and lows. The internal heat has two parts. Some fraction ofthe heat, estimated to be between 25% and 75%, originated from the gravitational energy releasedwhen the Earth formed. The other fraction of internal heat is produced by the decay of radioactiveelements, principally uranium, thorium, and potassium, in the Earth. The EarthÕs internal heatslowly decays over geologic time as it migrates to the surface and is radiated away into space. It isthis migration of heat out of the Earth that drives tectonic processes. Heat causes both the outer coreand the mantle to convect, as hot regions rise and cold regions sink. Convection within the outer coregives rise to the EarthÕs magnetic field, and may have other, as yet not understood, geologic conse-quences. Convection in the mantle is responsible for deformation of the EarthÕs crust as well as vol-canism.

2885 km2270 km

1216 kmMantleCore

Crust(~40 km)

Figure 1.11. The Earth in cross-section. The outer rockypart of the planet, the mantle and crust, consists princi-pally of silicates and is 2885 km thick. The core, di-vided into a liquid outer core and a solid inner core, con-sists of iron-nickel alloy and is 3486 km thick.



20 August 22, 1997

The great revolution in earth science in the 1960Õs centered on the realization that the outer part ofthe Earth was divided into a number of ÒplatesÓ that moved relative to one and other. Most tectonicprocesses, as well as most volcanism, occur at the boundaries between these plates. The outer part ofthe Earth, roughly the outer 100 km or so, is cool enough (<1000 ¡ C) that it is rigid. This rigid outerlayer is known as the lithosphere and comprises both the crust and the outermost mantle (Figure1.12).The mantle below the lithosphere is hot enough (and under sufficient confining pressure) that i tflows, albeit extremely slowly, when stressed. This part of the mantle is known as the astheno-sphere. Temperature differences in the mantle create stresses that produce convective flow. It is thisflow that drives the motion of the lithospheric plates. The motion of the plates is extremely slow, afew tens of centimeters per year at most and generally much less. Nevertheless, on geologic timescales they are sufficient to continually reshape the surface of the Earth, creating the AtlanticOcean, for example, in the last 200 million years.

Rather than thinking of plate motion as being driven by mantle convection, it would be more cor-rect to think of plate motion as part of mantle convection. Where plates move apart, mantle rises tofill the gap. As the mantle does so, it melts. The melt rises to the surface as magma and creates newoceanic crust at volcanos along mid-ocean ridges (Figure 1.12). Mid-ocean ridges, such as the East Pa-cific Rise and the Mid-Atlantic Ridge, thus mark divergent plate boundaries. As the oceanic crustmoves away from the mid-ocean ridge it cools, along with the mantle immediately below it. Thiscooling produces a steadily thickening lithosphere. As this lithosphere cools, it contracts and itsdensity increases. Because of this contraction, the depth of the ocean floor increases away from themid-ocean ridge. When this lithosphere has cooled sufficiently, after 100 million years or so, it be-comes more dense than the underlying asthenosphere. The lithosphere may then sink back into themantle in a process known as subduction. As the lithosphere sinks, it creates deep ocean trenches, suchas the Peru-Chile Trench, or the Marianas Trench. Chains of volcanos, known as island arcs, invaria-bly occur adjacent to these deep sea trenches. The volcanism occurs as a result of dehydration of thesubducting oceanic crust and lithosphere. Water released from the subducting oceanic crust rises intothe overlying mantle, causing it to melt. The island arcs and deep sea trenches are collectively calledsubduction zones. Subduction zones thus mark convergent plate boundaries. It is primarily the sinkingof old, cold lithosphere that drives the motion of plates. Thus the lithosphere does not merely rideupon convecting mantle, its motion is actually part of mantle convection.

The density of the continental crust is always lower than that of the mantle, regardless of howcold the crust becomes. As a result, it cannot be subducted into the mantle. The Indian-Eurasian plate

MId-Ocean Ridge

Subduction

Lithosphere Asthenosphere

Figure 1.12. Cross section of the Earth illustrating relationships betweenlithosphere and asthenosphere and plate tectonic processes. Oceanic crustand lithosphere are created as plates diverge at mid-ocean ridges and areeventually subducted back into the mantle. Continental lithosphere isthicker and lighter than oceanic lithosphere and not easily subducted.



21 August 22, 1997

boundary is a good example of what happens when two continental plates converge. Neither platereadily subducts and the resulting compression has produced, and continues to uplift, the HimalayanMountains and the Tibetan Plateau. This area of the continental crust is not only high, it is also deep.The crust beneath this region extends to depths of as much as 100 km, nearly three times the averagecrustal thickness. Rocks within this thickened crust will experience increased temperatures and pres-sures, leading to metamorphism, a process in which new minerals form in place of the original ones.In the deepest part of the crust, melting may occur, giving rise to granitic magmas, which will thenintrude the upper crust.

The topographically high Himalayas are subject to extremely high rates of erosion, and the riv-ers draining the area carry enormous quantities of sediment. These are deposited mainly in thenorthern Indian Ocean, building the Ganges and Indus Fans outward from the continental margin. Asthe mountains erode, the mass of crust bearing down on the underlying asthenosphere is reduced. As aresult of the decreased downward force, further uplift occurs.

The third kind of plate boundary is known as a transform boundary and occurs where plates slidepast one and other. A good example of this type of plate boundary is the San Andreas Fault system ofCalifornia. Here the Pacific Plate is sliding northward past the North American Plate. The pas-sage is not an easy one, however. The two plates occasionally stick together. When they do, stressessteadily build up. Eventually, the stress exceeds the frictional forces holding the plates together,and there is a sudden jump producing an earthquake. Earthquakes are also common in subduction zonesand along mid-ocean ridges. They are much rarer in the interior of plates.

Most volcanism and crustal deformation occur along plate boundaries. A small fraction of vol-canos, however, is located in plate interiors and appears to be entirely unrelated to plate tectonicprocesses. Crustal uplift also occurs in association with these volcanos. Two good examples are Ha-waii and Yellowstone. These phenomena are thought to be the result of mantle plumes. Mantleplumes are convective upwellings. In contrast to the convective upwelling occurring along mid-oceanridges, which is typically sheet-like, mantle plumes appear to be narrow (~100 km diameter) andapproximately cylindrical. Furthermore, it appears that mantle plumes rise from much deeper in themantle, perhaps even the core-mantle boundary, than convection associated with plate motion.

Earth Materials

The most abundant elements in the Earth are O and Fe (both close to 32%), Mg (~15%), Si (~14%),Ni (~1.8%), Ca (1.7%), and Al (1.6%). The majority of the EarthÕs Fe and Ni are in the core. The re-maining rocky part of the Earth, the mantle and crust, consists of ~44% O, ~23% Mg, 21% Si, 2.5% Ca,and 2.4% Al. As a consequence, the outer part of the Earth consists principally of compounds known assilicates. Silicates are compounds based on the silica tetrahedron, consisting of a silicon atom sur-rounded by four oxygens (Figure 11.13a). The bonds between the oxygens and silicon are about 50% co-valentÐ50% ionic and are quite strong. The silicon atom shares an electron with each of the four oxy-gens. Since oxygen has two valence electrons, each oxygen can form an additional bond. There are twopossibilities: the oxygen can form a second bond (which is usually more ionic) with another metalatom or it can form a bond with a second silicon. This latter possibility leads to linking of silicatetrahedra to form rings, chains, sheets, or frameworks. Oxygens bound to two silicons are calledbridging oxygens.

In orthosilicates, the silica tetrahedra are either completely independent or form dimers, that is,two linked tetrahedra. A good example of a mineral of this type is olivine, whose structure is illus-trated in Figure 11.13b. The chemical formula for olivine is (Mg,Fe)2SiO4. The notation (Mg,Fe) indi-cates that either magnesium or iron may be present. Olivine is an example of a solid solution betweenthe Mg-end member, forsterite (Mg2SiO4), and the Fe-end member, fayalite (Fe2SiO4). Such solid so-lutions are quite common among silicates. As the formula indicates, there are two magnesium or ironatoms for each silica tetrahedra. Since each Mg or Fe has a charge of +2, their charge balances the Ð4charge oÄ each silica tetrahedra. Olivine constitutes roughly 50% of the EarthÕs upper mantle, and isthus one of the most abundant minerals in the Earth. At great pressures, it disproportionates to a Fe-



22 August 22, 1997

Mg oxide (magnesiow�stite) and (Mg,Fe)SiO3 (Mg-perovskite). At the same time, silicon atoms be-come octahedrally coordinated (surrounded by 6 oxygens rather than 4 as in the silica tetrahedra).

In chain silicates, the silica tetrahedra are linked together to form infinite chains (Figure 1.13c),with one bridging oxygen per tetrahedra. Minerals of this group are known as pyroxenes and havethe general formula XSiO3 where X is some metal, usually Ca, Mg, or Fe, which is located betweenthe chains. Two pyroxenes, orthopyroxene ((Mg,Fe)SiO3) and clinopyroxene (Ca(Mg,Fe)Si2O6 arevery abundant in the EarthÕs upper mantle as well as mafic igneous rocks. The pyroxenes wollastonite(CaSiO3) and jadite (NaAlSi2O6) are found exclusively in metamorphic rocks.

In double chain silicates, an additional bridging oxygen per tetrahedra joins two chains together.Minerals of this group areknown as amphiboles ,which occur widely in bothigneous and metamorphicrocks. Among the importantminerals in this group arehornblende (Ca2Na(Mg,Fe)4

Al3Si8O22(OH)2), tremolite-actinolite (Ca2(Mg,Fe)5Si8

O22(OH)2), and glaucophane(Ca2(Mg,Fe)3Al3Si8O22(OH)2) .These minerals all containOH as an essential compo-nent (Cl or F sometimes sub-stitutes for OH). They arethus examples of hydroussilicates.

Sharing of a third oxy-gen links the tetrahedrainto sheets, forming thesheet silicates (Figure1.13d). This group includesmicas such as biotite(K(Mg,Fe)3AlSi3O10(OH)2)and muscovite (KAl3Si3O10

(OH)2), talc (Mg3Si4O10

(OH)2), and clay mineralssuch as kaolinite (Al2Si2O5

(OH)4). As in amphiboles,OH is an essential compo-nent of sheet silicates.These minerals can formthrough weathering and arethus primary sedimentaryminerals. Many of them arefound in igneous and meta-morphic rocks as well.

When all four oxygensare shared between tetra-hedra, the result is aframework. The simplestframework silicate isquartz(SiO2), which con-

a

The Silica TetrahedronSheet Structure

d

Oxygen Silicon Mg, Fe, etc.

c

bridgingoxygens

non-bridgingoxygens

Pyroxene Structure

b

Olivine Structure

Figure 1.13. The silica tetrahedron and the structure of silicate miner-als. a. The silica tetrahedron consists of a central silicon atom boundto 4 oxygens. b. In orthosilicates such as olivine, the tetrahedra areseparate and each oxygen is also bound to other metal ions that occupyinterstitial sites between the tetrahedra. c. In pyroxenes, the tetra-hedra each share one oxygen and are bound together into chains.Metal ions are located between the chains. d. In sheet silicates, suchas talc, mica, and clays, the tetrahedra each share 3 oxygens and arebound together into sheets.



23 August 22, 1997

sists solely of linked SiO4 tetrahedra. The other important group of framework silicates are thefeldspars, of which there are three end-members: sanidine (KAlSi3O8), albite (NaAl Si3O8), andanorthite (Ca Al2Si2O8). The calcium and sodium feldspars form the plagioclase solid solution,which is stable through a large temperature range. Sodium and potassium feldspars, collectivelycalled alkali feldspar, form more limited solid solutions. Feldspars are the most abundant mineralsin the EarthÕs crust. Silicates are the most abundant minerals in the Earth, but not the only ones. Other classes of min-erals include oxides such as magnetite (Fe3O4) and ilmenite (FeTiO3), carbonates such as calcite(CaCO3), sulfates such as gypsum CaSO4

.2H2O, hydroxides such as gibbsite (Al(OH)3), and sulfidessuch as pyrite FeS2.

References and Suggestions for Further Reading

Gribbin, J. R. 1984. In Search of Schr�dinger's Cat: Quantum Physics and Reality. New York: BantamBooks.

Other Texts in Geochemistry:

Broecker, W. S. and V. M. Oversby, 1971. Chemical Equilibria in the Earth. New York: McGraw-Hil l .

Henderson, P. 1986. Inorganic geochemistry. Oxford: Pergamon Press.Richardson, S. M. and H. Y. McSween. 1988. Geochemistry: Pathways and Processes. New York:

Prentice Hall.Brownlow, A. H. 1996. Geochemistry. New York: Prentice Hall.Krauskopf, K. B. and D. K. Bird. 1995. Introduction to Geochemistry. New York: McGraw-Hill.

w . m . w h i t e g e o c h e m i s t r y chapter 1:...

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